Assumption Of Perfect Mixing Research Articles

Tubular photobioreactor design based on mixing intensity

A novel design methodology for tubular photobioreactors (TPBRs) for the mass culture of microalgae that can account for mixing intensity is presented. To date, TPBRs have been mainly designed and operated under the assumption of perfect mixing with regard to photosynthesis performance (light integration regime). In this work we show that this simplification has been leads to significant errors in the prediction of the optimal dilution rate and biomass productivity. To this end, computational fluid dynamics and light distribution model have been employed to calculate the trajectories and light histories I(t) of a microalgal cell population represented by 50 particles of 5 μm diameter. The density of the microalgal cells was set at 1000 kg m−3 and the tube diameters (D) were 14, 24, 44, 64 and 84 mm, with the circulation velocities (v) ranging from 0.4 to 1 m s-1. This has been coupled to a dynamic photosynthesis model in order to calculate the average photosynthetic response and hence the integration factors in TPBRs. It has been demonstrated that for a generic microalgal strain, the use of the light integration simplification (Γ = 1) would result in the prediction of an optimal dilution rate of 0.0315 h−1 (for D = 14 mm and v = 0.4 m/s as an example), which would lead to an actual biomass productivity of 182.5 g biomass m−3h−1 if the predicted integration factor (Γ = 0.578) is used whereas the newly proposed method predicts an optimal dilution rate of 0.0125 h−1 and a biomass productivity of 362.3 g biomass m−3h−1. This demonstrates that simplifying the light integration regime is inadequate for TPBRs design and operation, resulting in significant inaccuracies. The estimation charts and regressions proposed in this work to estimate actual integration factors will enable the development of an optimization method for TPBRs based on mixing intensity.

Electrolyte Gradients and Capacity Drop in Large Flow Battery Tanks: From Experiments to Fluid-Dynamic Investigations

A study of the effects of electrolyte flow inside the tanks on electrical performance of an industrial-size Vanadium Redox Flow Battery (VRFB) is presented. The concentration of electrolytes feeding the stacks of VRFBs is crucial in determining the device voltage and overall power performance. Usually, the assumption of perfect mixing in the tanks is assumed, but the hydraulic behavior of large VRFB can deviate significantly from this assumption depending on the electrolyte flow rate, stochiometric factor and geometry of the tanks. In this study, the State of Charge (SoC) measurements have been analyzed, starting from the signal produced by an Open Circuit Voltage (OCV) cell. An experimental campaign has been conducted during charge/discharge roundtrip cycles at different current levels and constant stoichiometric factor. Building on the delay in the voltage response of the battery, a fluid-dynamic model was developed to study how the hydraulic behavior of electrolytes inside tanks influences the electrolyte concentration and, consequently, the SoC of the electrolyte that feeds the stack and the electrical time response of the battery. The model indicated that a stratification of charged electrolyte is responsible for this delay resulting in an initial voltage plateau. A different hydraulic behavior was found in each tank and in each charge/discharge phase. These results highlight the tank role in the industrial-scale VRFB performance. References Sanchez-Diez, E. Ventosa, M. Guarnieri, A. Trovò, C. Flox, R. Marcilla, F. Soavi, P. Mazur, E. Aranzabe, R. Ferret, “Redox flow batteries: status and perspective towards sustainable stationary energy storage”, J. Power Sources, 481, (2021) 228804.Kurilovich, A. Trovò, M. Pugach, K. J. Stevenson, M. Guarnieri. Prospect of Modeling Industrial Scale Flow Batteries – from Experimental Data to Accurate Overpotential Identification, Renew. Sust. Energ. Rev. 167, (2022) 112559.Trovò, V. Di Noto, J. E. Mengou, C. Gambaro, M. Guarnieri. Fast Response of kW-Class Vanadium Redox Flow Batteries, IEEE Trans. Sustain. Energy 12, (2021) 2413–2422.Trovò, M. Rugna, N. Poli, M. Guarnieri. Prospects for industrial vanadium flow batteries, Ceram. Int., 49 (14), (2023) 24487-24498.Maggiolo, A. Trovò, M. Guarnieri, “Reactant Flow in Flow Batteries”, in L. Cabeza (ed.), Encyclopedia of Energy Storage, vol. 4, pp. 231-242. Oxford: Elsevier. March 2022.A. Prieto-Díaz, S. E. Ibáñez, M. Vera. Fluid dynamics of mixing in the tanks of small vanadium redox flow batteries: Insights from order-of-magnitude estimates and transient two-dimensional simulations, Int. J. Heat Mass Transf. 216, (2023) 124567.Trovò, N. Poli, M. Guarnieri. New strategies for the evaluation of Vanadium Flow Batteries: testing prototypes, Cur. Opin. Chem. Eng. 37, (2022) 100853. Figure 1

A GPU-accelerated computational fluid dynamics solver for assessing shear-driven indoor airflow and virus transmission by scale-resolved simulations

We explore the applicability of MATLAB for 3D computational fluid dynamics (CFD) of shear-driven indoor airflows. A new scale-resolving, large-eddy simulation (LES) solver titled DNSLABIB is proposed for MATLAB utilizing graphics processing units (GPUs). In DNSLABIB, the finite difference method is applied for the convection and diffusion terms while a Poisson equation solver based on the fast Fourier transform (FFT) is employed for the pressure. The immersed boundary method (IBM) for Cartesian grids is proposed to model solid walls and objects, doorways, and air ducts by binary masking of the solid/fluid domains. The solver is validated in two canonical reference cases and against experimental data. Then, we demonstrate the validity of DNSLABIB in a room geometry by comparing the results against another CFD software (OpenFOAM). Next, we demonstrate the solver performance in several isothermal indoor ventilation configurations and the implications of the results are discussed in the context of airborne transmission of COVID-19. The novel numerical findings using the new CFD solver are as follows. First, a linear scaling of DNSLABIB is demonstrated and a speed-up by a factor of 3-4 is also noted in comparison to similar OpenFOAM simulations. Second, ventilation in three different indoor geometries are studied at both low (0.1 m/s) and high (1 m/s) airflow rates corresponding to Re=5000 and Re=50000. An analysis of the indoor CO2 concentration is carried out as the room is emptied from stale, high CO2 content air. We estimate the air changes per hour (ACH) values for three different room geometries and show that the numerical estimates from 3D CFD simulations differ by 80%–150% (Re=50000) and 75%–140% (Re=5000) from the theoretical ACH value based on the perfect mixing assumption. Third, the analysis of the CO2 probability distributions (PDFs) indicates a relatively non-uniform distribution of fresh air indoors. Fourth, utilizing a time-dependent Wells-Riley analysis, an example is provided on the growth of the cumulative infection risk which is shown to reduce rapidly after the ventilation is started. The average infection risk is shown to reduce by a factor of 2 for lower ventilation rates (ACH=3.4-6.3) and 10 for the higher ventilation rates (ACH=37-64). Finally, we utilize the new solver to comment on respiratory particle transport indoors. A key contribution of the paper is to provide an efficient, GPU compatible CFD solver environment enabling scale-resolved simulations (LES/DNS) of airflow in large indoor geometries on a single GPU designed for high-performance computing. The demonstrated efficacy of MATLAB for GPU computing indicates a high potential of DNSLABIB for various future developments on airflow prediction.

Experimental and Numerical Study of Electrolyte Mixing in the Tanks of Vanadium Redox Flow Batteries: Insights from Conventional and 3D-Printed Tanks

Vanadium redox flow batteries (VRFBs) are a promising technology for large-scale grid energy storage. Despite extensive research on the electrochemical and fluid dynamic phenomena in the cells or stacks [1, 2], the impact of electrolyte flow and mixing in the tanks has received much less attention. Previous research has shown that the cell potential and battery capacity may substantially differ from those predicted under the perfect mixing assumption [3] (i.e., continuous stirred-tank reactor). Recent numerical simulations have detected the formation of segregated zones within the tanks that cause inhomogeneous electrolyte utilization and significant capacity decay [4]. The authors have confirmed these results by means of transient laminar numerical simulations [5] and experimental testing of an industrial VRFB system [6]. However, these first attempts should be carefully extended, using a well-controlled lab-scale system, so that the effects of the different components can be independently studied.In this study, we investigate the effect of electrolyte mixing on VRFB response using a medium-size lab-scale system. Two experimental campaigns were conducted to explore i) the impact of flow rate and applied current on the predicted fluid behavior, and ii) the performance of 3D-printed tanks designed for improving electrolyte mixing with reduced dead recirculation zones. In both campaigns, the transient response of the system was investigated to assess the effect of electrolyte mixing on battery performance. The experimental results were also compared with numerical simulations, which showed good agreement with the experimental data.This work makes a novel contribution to the field by using 3D-printed tanks to investigate the impact of electrolyte mixing on RFB performance. The results extend previous research on this topic and provide insights into the design of RFBs for improved energy storage. Specifically, the use of 3D-printed tanks could be a promising approach to address the issue of inhomogeneous electrolyte exploitation in RFBs. The findings of this study could serve in the design of RFBs for large-scale grid energy storage and facilitate the adoption of this technology as a sustainable energy storage solution.

Optimizing the Electrolyte Mixing in Industrial Tanks of Vanadium Redox Flow Batteries

Redox flow batteries (RFB) are an emerging technology for large-scale grid energy storage. Different approaches have been adopted to investigate the operation of RFBs, such as experimental testing and mathematical modelling of the electrochemical cells [1]. However, the effect of the flow and mixing in the electrolyte tanks on the performance of RFBs has been largely overlooked and only recently has started to receive some attention [2]. In a recent work, the authors used numerical simulations to show how the fluid dynamics of the electrolytes within small lab-scale tanks can lead to different flow behaviors depending on whether forced or natural convection is dominant. The irregular transient mixing of the electrolyte in the tanks modifies both the cell potential and battery capacity with respect to those predicted under the widely used perfect mixing assumption (i.e., continuous stirred-tank reactor) [3]. However, this first attempt relied on several simplifying assumptions, such as two-dimensional geometries under small-cell (i.e., laminar) flow conditions, and thus provided only a qualitatively understanding of the flow in the tanks.This work exploits the idea of using CFD simulations to investigate the effect of operating conditions on the electrolyte flow in the tanks and its impact on battery response, focusing on high capacity industrial tanks with high (i.e., turbulent) flow rates and less restrictive simplifying assumptions. Our numerical simulations show how turbulence improves mixing, but also produces quasi-steady flows where a turbulent jet crosses the tank leaving dead electrolyte regions. Different tank solutions are presented aiming to improve the mixing and increase the capacity of the battery, playing both with the tank geometry and the operating conditions. Results on the charging and discharging operations, cell potential and electrolyte mixing index are presented and discussed. Acknowledgments This work has been partially funded by FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación Projects PID2019-106740RB-I00 and RTC-2017-5955-3/AEI/10.13039/501100011033, and by Grant IND2019/AMB-17273 of the Comunidad de Madrid.

Stepping beyond perfectly mixed conditions in soil hydrological modelling using a Lagrangian approach

Abstract. A recent experiment of Bowers et al. (2020) revealed that diffusive mixing of water isotopes (δ2H and δ18O) over a fully saturated soil sample of a few centimetres in length required several days to equilibrate completely. In this study, we present an approach to simulate such time-delayed diffusive mixing processes, on the pore scale, beyond instantaneously and perfectly mixed conditions. The diffusive pore mixing (DIPMI) approach is based on a Lagrangian perspective on water particles moving by diffusion over the pore space of a soil volume and carrying concentrations of solutes or isotopes. The idea of DIPMI is to account for the self-diffusion of water particles across a characteristic length scale of the pore space using pore-size-dependent diffusion coefficients. The model parameters can be derived from the soil-specific water retention curve, and no further calibration is needed. We test our DIPMI approach by simulating diffusive mixing of water isotopes over the pore space of a saturated soil volume using the experimental data of Bowers et al. (2020). Simulation results show the feasibility of the DIPMI approach for reproducing the measured mixing times and concentrations of isotopes at different tensions over the pore space. This result corroborates the finding that diffusive mixing in soils depends on the pore size distribution and the specific soil water retention properties. Additionally, we perform a virtual experiment with the DIPMI approach by simulating mixing and leaching processes of a solute in a vertical, saturated soil column and compare the results against simulations with the common perfect mixing assumption. The results of this virtual experiment reveal that the frequently observed steep rise and long tailing of breakthrough curves, which are typically associated with non-uniform transport in heterogeneous soils, may also occur in homogeneous media as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.

An experimental application of laser-scattering sensor to estimate the traffic-induced PM2.5 in Beijing.

Traffic-induced air pollutant emissions are currently rising rapidly. However, measurement of the roadside environment and calculation of the emission factors for traffic-induced PM2.5 are restricted to certain locations and periods due to the limitations of conventional air monitoring techniques. This paper introduces a portable sensor package with a laser light-scattering PM2.5 sensor and an electrochemical CO sensor to measure roadside PM2.5 and CO concentrations. The low-cost sensor package underwent local calibration using reference instruments at the Chinese Research Academy of Environmental Sciences (CRAES). The results showed a high level of correlation (r in the range of 0.94-0.95 and 0.81-0.83 for PM2.5 and CO, respectively) between measurements using the sensor packages and those measured by the reference equipment. The study found that the low-cost sensor packages were able to deliver reliable measurements of PM2.5 and CO concentrations. Four low-cost sensor packages were deployed along a short section of an expressway to measure roadside PM2.5 and CO concentrations. The directly measured concentrations were firstly calibrated with the temperature and humidity. The corrected PM2.5 concentrations from each side of the road were different, while the corrected CO concentrations were similar on both sides of the road. Therefore, only the PM2.5 measurements were applied in this study's box model. The assumption of perfect mixing in order for the box model to be applied was shown by the results to be valid to some extent. The PM2.5 emission factors for opposite sides of the road should be calculated separately based on the direction of traffic flow. The PM2.5 emission factors calculated in this study were variable, being impacted by traffic conditions and meteorological conditions. The paper presents a method for obtaining PM2.5 emission factors based on a box model. This method is a promising way of monitoring air pollution in the roadside environment.

Developing a new passive tracer gas test for air change rate measurement

Ventilation is critical in interpreting indoor air quality (IAQ), yet most IAQ assessments do not report ventilation adequately. Most ventilation assessments use tracer gas tests (TGT) to measure total air change rate (ACH), but currently applied TGTs present three shortcomings: limited comparability between ACH and IAQ data, inadequate substances employed as tracer gases and tendency to bias arising from perfect-mixing assumption. This paper proposes a new TGT approach, employing an alternative tracer gas that is captured/analysed using commercial passive IAQ-samplers and including a careful planning-phase to account for imperfect-mixing. Two substances were selected as potential alternative tracers: 2-butoxyethyl-acetate (EGBEA) and deuterated decane (D-decane). Tracer-source tests were performed in lab, enabling enhancements to the source design. Results indicated RH influence over the emissions rates, and EGBEA’s use as tracer was discarded due to hygroscopy. Further work includes evaluating D-decane’s behaviour under varying conditions and computer-simulating TGTs to study the imperfect-mixing effects.

Long-time simulation of catalytic MTO reaction in a fluidized bed reactor with a coarse-grained discrete particle method — EMMS-DPM

Long-time behaviors widely exist in gas–solid reactors, e.g., the coke deposition and catalyst deactivation in the methanol to olefins (MTO) process. Due to the limitation of the computational cost, previous simulations of MTO reactors were mainly conducted with two-fluid model at short-time scales and assumed that the catalyst are perfectly mixed. Efficient simulation methods are, therefore, highly desirable, even for evaluating the assumptions through very long-time investigation. In this study, the MTO reaction kinetics is incorporated into a coarse-grained discrete particle method, namely EMMS-DPM, to simulate a pilot-scale reactor for 8 h of physical time. The simulation is validated by comparing the obtained gaseous products and coke contents with the experimental data. The perfect mixing assumption is validated by observing the residence time distribution of the catalyst for the whole reactor. The detailed coke content could provide more accurate data for accelerating steady state simulations. Furthermore, the relation between the coke content and age of the catalyst is directly obtained for the first time, which is valuable to effective use of the catalyst before discharging. The coke content is positively correlated to the age, but is also influenced by local conditions. For example, near the distributor, the catalyst particles are not well mixed and the maximum reaction rate fluctuates significantly even at large time scales. Thus, long-time particle-scale simulation would provide more dynamic details to characterize the reaction in the critical regions of the reactor, thus being very helpful to optimize operating conditions and the reactor designs.

Insights into advanced ball mill modelling through discrete element simulations

Important advances have been made in understanding ball milling during the last 25 years or so, a great part of it owing to the widespread application of the discrete element method (DEM), which is now an integral part of several advanced ball mill models. These models, however, must rely on assumptions regarding the mill mechanical environment that can help make the problem more manageable. The paper analyzes the validity of some assumptions that have been the basis of several advanced ball mill models by conducting DEM simulations of dry batch mills including both grinding media and particles. The validity of the assumption of perfect mixing of grinding media and particles, as well as of simulating exclusively the grinding media in order to collect the collision energy information for prediction of breakage and, thus, saving computational effort, are analyzed in great detail. It is concluded that the assumption of perfect mixing in the radial direction is generally valid, except for mill frequencies that are unusually high and exceedingly large ratios of mean ball and particle sizes being ground. It is also observed that a fraction of the number of collisions inside the mill do not involve particles, so that an empirical expression that is based on the ratio of surface areas of the ball and particle charge is proposed to estimate such proportion of unsuccessful collisions. Finally, a model from the authorś laboratory, that assumes that each collision in the mill will involve a monolayer bed of particles, is tested, demonstrating reasonable agreement when compared to simulations.

Catalytic Gasification – A Critical Analysis of Carbon Dioxide Methanation on a Ru/Al2O3 Catalyst

Abstract This paper proposes a corrected kinetic model for the Sabatier (CO2 Methanation) reaction. Several other kinetic studies have been performed on the Sabatier reaction to date; however, many of these studies contain simplifications. Data available from one of the first studies (Lunde, P.J., and F.L. Kester. 1974. “Carbon Dioxide Methanation on a Ruthenium Catalyst.” Industrial & Engineering Chemistry Process Design and Development 13 (1): 27–33) was utilized to perform a new analysis of the kinetics of CO2 Methanation. This work examined two models for the Sabatier reaction, the Perfect Mixing assumption and the differential (conversion) reactor assumption. After available data was screened for the occurrence of the Reverse Water Gas Shift reaction, the differential (conversion) reactor assumption was validated. A critical comparison to similar models available in literature is also presented.

Estimation of Filtration Efficiency – from Simple Correlations to Digital Fluid Dynamics

AbstractAerosol filtration in fibrous filters is one of the principal methods of accurate removal of particulate matter from a stream of gas. The classical theory of depth filtration of aerosol particles in fibrous structures is based on the assumption of existing single fibre efficiency, which may be used to recalculate the overall efficiency of entire filter. Using “classical theory” of filtration one may introduce some errors, leading finally to a discrepancy between theory and experiment. There are several reasons for inappropriate estimation of the single fibre efficiency: i) neglecting of shortrange interactions, ii) separation of inertial and Brownian effects, ii) perfect adhesion of particles to the fibre, iv) assumption of perfect mixing of aerosol particles in the gas stream, v) assumption of negligible effect of the presence of neighbouring fibres and vi) assumption of perpendicular orientation of homogenous fibres in the filtration structure. Generally speaking, “classical theory” of filtration was used for characterization of the steady - state filtration process (filtration in a clean filter, at the beginning of the process) without deeper investigation of the influence of the nternal structure of the filter on its performance. The aim of this review is to outline and discuss the progress of deep-bed filtration modelling from the use of simple empirical correlations to advanced techniques of Computational Fluid Dynamics and Digital Fluid Dynamics.

Variables sampling plans using composite samples for food quality assurance

Testing composite samples is a useful strategy to achieve sampling economy. Several studies have shown the effectiveness of this technique under the assumption of perfect mixing of primary samples. This paper investigates the effect of imperfect composite sample preparation on the performance of two and three-class variables sampling inspection plans, and identifies scenarios in which testing composite samples is not advantageous. The design of sampling plans using composite samples is discussed and an implementation guide based on two points of the OC curve for perfect and imperfect mixing is provided.

Pore-scale simulation of microbial growth using a genome-scale metabolic model: Implications for Darcy-scale reactive transport

Recent advances in microbiology have enabled the quantitative simulation of microbial metabolism and growth based on genome-scale characterization of metabolic pathways and fluxes. We have incorporated a genome-scale metabolic model of the iron-reducing bacteria Geobacter sulfurreducens into a pore-scale simulation of microbial growth based on coupling of iron reduction to oxidation of a soluble electron donor (acetate). In our model, fluid flow and solute transport is governed by a combination of the Navier–Stokes and advection–diffusion–reaction equations. Microbial growth occurs only on the surface of soil grains where solid-phase mineral iron oxides are available. Mass fluxes of chemical species associated with microbial growth are described by the genome-scale microbial model, implemented using a constraint-based metabolic model, and provide the Robin-type boundary condition for the advection–diffusion equation at soil grain surfaces.Conventional models of microbially-mediated subsurface reactions use a lumped reaction model that does not consider individual microbial reaction pathways, and describe reactions rates using empirically-derived rate formulations such as the Monod-type kinetics. We have used our pore-scale model to explore the relationship between genome-scale metabolic models and Monod-type formulations, and to assess the manifestation of pore-scale variability (microenvironments) in terms of apparent Darcy-scale microbial reaction rates. The genome-scale model predicted lower biomass yield, and different stoichiometry for iron consumption, in comparison to prior Monod formulations based on energetics considerations. We were able to fit an equivalent Monod model, by modifying the reaction stoichiometry and biomass yield coefficient, that could effectively match results of the genome-scale simulation of microbial behaviors under excess nutrient conditions, but predictions of the fitted Monod model deviated from those of the genome-scale model under conditions in which one or more nutrients were limiting.The fitted Monod kinetic model was also applied at the Darcy scale; that is, to simulate average reaction processes at the scale of the entire pore-scale model domain. As we expected, even under excess nutrient conditions for which the Monod and genome-scale models predicted equal reaction rates at the pore scale, the Monod model over-predicted the rates of biomass growth and iron and acetate utilization when applied at the Darcy scale. This discrepancy is caused by an inherent assumption of perfect mixing over the Darcy-scale domain, which is clearly violated in the pore-scale models. These results help to explain the need to modify the flux constraint parameters in order to match observations in previous applications of the genome-scale model at larger scales. These results also motivate further investigation of quantitative multi-scale relationships between fundamental behavior at the pore scale (where genome-scale models are appropriately applied) and observed behavior at larger scales (where predictions of reactive transport phenomena are needed).

Exact equilibrium-state solution of an intracellular complex formation model:kA↔Preaction in a small volume

A generic model of complex formation in small volumes was studied under the assumption of perfect mixing. Particles A react in clusters, and each reaction converts k A particles into a P particle. The back reaction is also allowed. The equilibrium state of the model is solved exactly. Fluctuations in product particle number are reduced by increasing the degree of cooperativity k. Three qualitatively distinct reactant fluctuation characteristics emerge.

Explosion hazards related to hydrogen releases in nuclear facilities

Hydrogen explosion risk needs to be carefully assessed and evaluated in nuclear facilities because of the potential catastrophic consequences: breakdown of safety equipments, failure of containment, dissemination of radioactive materials in the environment. When studying an indoor release, one possible simplification is to assume a perfect gas mixing inside the room. This assumption is effectively often used to evaluate toxic risks in the environment outside a building ( Mastellone, Ponte, & Arena, 2003). However, perfect gas mixing assumption is only a rough approximation, as indoor concentrations can largely differ from mean values, due to buoyancy, recirculation zones or obstacles for example. In order to better evaluate the risk of explosion in case of an accidental release of hydrogen, IRSN conducted a numerical study using FLACS CFD software. Several parameters have been studied to identify dangerous situations and draw a representative picture of the risk: room size, position and direction of hydrogen leak, ventilation characteristics. Hydrogen release flow rates used for numerical simulations have been chosen as the highest leak rate which, by applying the assumption of perfect mixing, produces an average concentration in the room equal to hydrogen lower flammability limit (LFL). Simulation results indicate that in some particular configurations, especially for impinging hydrogen jets, hydrogen concentrations can locally be above LFL and then create explosive atmospheres with significant volumes.

Pore-Network Modeling Dedicated to the Determination of the Petrophysical-Property Changes in the Presence of Reactive Fluid

Summary A pore-network model (PNM) is an efficient tool to account for phenomena occurring at the pore scale. Its explicit 3D network of pores interconnected by throats represents an easy way to consider the topology and geometry effects on upscaled and homogenized petrophysical parameters. In particular, this modeling approach is appropriate to study the rock/fluid interactions. It can provide quantitative information both on the effective transport property modifications caused by the reactions and on the structure evolution resulting from dissolution/precipitation mechanisms. The model developed is based on the resolution of the macroscopic reactive transport equation between the nodes of the network. By upscaling the results, we then determined the effective transport properties at the core scale. A sensitivity study on reactive and flow regimes has been conducted in the case of single-phase flow in the limit of long times. It has been observed that the mean reactive solute velocity and dispersion can vary up to one order of magnitude compared with the tracer values because of the concentration-profile heterogeneity at the pore scale resulting from the surface reactions. As for the reactive apparent coefficient, when the kinetics is limited by the mass transfer, it can decrease by several orders of magnitude with regard to that calculated by the usual perfect-mixing assumption. That is why scale factors should be added to the classical macroscopic transport equation implemented in reservoir simulators to predict accurately the reactive flow effects. For each study case, we also obtained the permeability variation vs. the porosity evolution in a physical way that accounts for reactive transport conditions. It appears that the wall-deformation pattern and its effect on petrophysical properties must be explained by considering both microscopic and macroscopic scales of the reactive transport, each one governed by a dimensionless number comparing reaction and transport characteristic times. This work helps improve the understanding of surface-reactions effects on reactive flow on the one hand and on permeability and porosity modifications on the other. Using the PNM approach, scale-factor parameters and permeability-vs.-porosity relations can be determined for various rock types and reactive flow regimes. Once integrated as inputs in a reservoir simulator, these relations form a powerful and convenient means of enhancing the modeling accuracy of the change in petrophysical properties during injection of a reactive fluid, such as brine rich in carbon dioxide (CO2).

Energy Estimation on CRN Process of Fly Ash as a Slow-Release Nitrogen Fertilizer

Through carbothermal reduction and nitridation (CRN) reaction, nitrogen could be fixed into fly ash up to 28 wt %. Nitrided fly ash has the potential to be a source of slow release nitrogen fertilizer. To further investigate this potential, the energy consumptions were estimated for the nitridation process of fly ash. Reactors such as parallel rotary furnaces were simulated for the heat loss of radiation and convection. Material balance was carried out to determine the dimension of the rotary furnaces. Subsequently, on the basis of the dimension of the rotary furnace, the energy balance was performed from the reaction engineering aspects of the nitridation reaction of fly ash. Ultimately, the total energy was transformed into per unit nitrogen and compared with the energy consumption of the Haber-Bosch process for ammonia synthesis. The energy balance calculation suggested that there is great potential for nitrided fly ash to be slow release nitrogen fertilizer. 1. Introduction Coal fly ash is the incomplete combustion product from a coal-fired power plant. Currently, coal is the major source of fossil energy in mainland China. The electricity generated from coal-fired power plants accounts for 80% of the power nationwide. This situation will remain unchanged over a long period of time. Consequently, the amount of coal fly ash shall continue to increase steadily, accounting for 15-40% of the mass of coal. The proper disposal or utilization of coal fly ash brings a great challenge to the environment. Scientists have long been dedicated to exploiting novel applications of fly ash, such as construction material, 1 flocculant, 2 absorbent, 3 low-value-added ceramics, 3 soil amendment, 4,5 and so on. We had previously demonstrated successful introduction of nitrogen into fly ash via CRN (carbothermal reduction and nitridation) reactions. 6 We had also elaborated the prospect of nitrided fly ash in application as a source of slow-release nitrogen fertilizer from the aspect of reaction kinetics. 7-9 Currently, the most widely used nitrogen fertilizers are mainly based on ammonia synthesized from the Haber-Bosch process. Those commercial nitrogen fertilizers have the drawback of low efficiency due to high solubility in water. In comparison, nitrogen could be incorporated into fly ash as high as 28 wt % 6 and slowly released in the form of ammonia through hydrolysis process. 10 Nevertheless, reasonable energy consumption is essential for any further potential application of fly ash. Accordingly, this study presents the energy estimation for CRN reaction of fly ash. The estimated energy was compared with the energy consumed by the Haber-Bosch process to prepare ammonia. The comparison reveals great potential in application of fly ash as a source of nitrogen fertilizer. From the aspects of reaction engineering, the energy consumption was evaluated by material and energy balance calculations from preliminary design of the rotary furnace reactors. Rotary tube reactors have the advantage that precursor powder or aggregates are continuously replaced at the furnace tube wall, thus providing superior and more uniform heattransfer characteristics relative to fixed bed reactors or moving bed reactors. 11 Residence times are shorter (typically 30 min to a few hours) than in moving beds. In this study on gas-solid reaction in rotary furnaces, a countercurrent flow was chosen. Although many furnaces experience considerable difficulty in achieving uniform product, virtually all of the rotary furnace models are based on an assumption of perfect mixing in an angular direction. The assumption depicts that, at each axial position along the furnace, the bed is well-mixed in the transverse plane; i.e., the bed material is isothermal over any transverse section of furnace. Heat transfer within the bed reactants occurs by the same mechanisms as in any packed bed, i.e., particle-to-particle conduction, radiation, and interstitial gas-to-particle convection. 12 Steady state was assumed throughout the calculation. The nitridation reaction conditions for scaling-up are shown in Table 1 from our previous publications. 6 A more quantitative understanding of the mass balance and heat-transport phenomena within the bed material are presented hereafter.

Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry

In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging from systems biology approaches, through network analysis (motif identification) towards developing language and simulators for low level biochemical processes. Apart from simulation work, much of the efforts are directed to using mean field equations (equivalent to the equations of classical chemical kinetics) to address various problems (stability, robustness, sensitivity analysis, etc.). Rarely is the use of mean field equations questioned. This review will provide a brief overview of the situations when mean field equations fail and should not be used. These equations can be derived from the theory of diffusion controlled reactions, and emerge when assumption of perfect mixing is used.

Experimental Verification of Incomplete Solute Mixing in a Pressurized Pipe Network with Multiple Cross Junctions

Water quality models based on accurate mixing data at cross junctions are important for estimating concentrations of chemical species in municipal water distribution systems. Recent studies indicate that the instantaneous complete (thus “perfect”) mixing assumption potentially can result in an erroneous prediction of water quality. The present study examines the updated “incomplete” solute mixing model at cross junctions in a network having multiple cross junctions. The model performance in predicting solute transport was evaluated through a series of tracer experiments in a pressurized 5×5 network with 9 cross junctions. The perfect mixing model consistently overestimated solute dilution at cross junctions and predicted evenly distributed solute concentration throughout the network. In contrast, the incomplete mixing model demonstrated uneven distribution patterns with a distinct solute plume, and the corresponding results were significantly more accurate than those based on the perfect mixing assumption...